A circular road is constructed outside a square field. The perimeter of the square field is 200 ft. If the width of the road is 7√2 ft. and cost of construction is Rs. 100 per sq. ft. Find the lowest possible cost to construct 50% of the total road.

Question

A circular road is constructed outside a square field. The perimeter of the square field is 200 ft. If the width of the road is 7&radic;2 ft. and cost of construction is Rs. 100 per sq. ft. Find the lowest possible cost to construct 50% of the total road.

Accepted Answer

Rs. 125,400 — âââââââ Radius of inner circle = &frac12; &times; diagonal of the square = 25&radic;2 cm Radius of outer circle = Radius of inner circle + width of the road = 32 cm 50% of the area of the road = 1 2 &times; &pi; &times; ( 32 2 ) 2 - ( 25 2 ) 2 = 1254 cm 2 Cost = 1254 &times;100 = Rs. 125,400 Hence, option (b).

XAT 2015 — QA & DI Question 7

Answer & solution